Aim: How do we use the normal distribution as an approximation for binomial probabilities?
At the end of the lesson, you will be able to...
interpret the area under the bell curve as a probability
interpret a binomial probability as a histogram and an approximation of the normal curve
find the mean and standard deviation of a binomial distribution
use the graphing calculator's normal cumulative density function feature (normalcdf) to approximate probabilities of Bernoulli trials involving "at least" and "at most".
This is a way to use the normal distribution to find probability. It's just another way of doing probability without using combinations. We use fractions (Bernoulli's) for exact answers and we can use this method for approximation.
This video shows one way how to find probability using the graphing calculator
In this video, Len talks about using the "table". We don't use the table. Ignore "table talk" but watch the steps for entering the information into a calculator
And...one more example
Classwork: Answer the following questions. Use your graphing calculator to help you.
**Sometimes all the information you need is not given to you. You may need to use the following to help you use the calculator:
The mean is the number of trials(n) times the probability of successes (p)
The standard deviation is sqrt of np(1-p)
a. Find the probability of getting at least 60 heads with 100 flips of a coin (Ans: 0.0287164928)
b. The probability that a team will win a game is 3/5. Use the normal distribution to estimate the probability that the team will win at least 10 of its next 25 games. (Ans:0.9876183243)
Homework: 3-23 odd. Your your graphing calculator to help you find your answers
Journal entry: Give an example of an experiment where it is appropriate to use a normal distribution as a approximation for a binomial probability. Explain why in this example an approximation of the probability is a better approach than finding the exact probability.
At the end of the lesson, you will be able to...
This is a way to use the normal distribution to find probability. It's just another way of doing probability without using combinations. We use fractions (Bernoulli's) for exact answers and we can use this method for approximation.
This video shows one way how to find probability using the graphing calculator
In this video, Len talks about using the "table". We don't use the table. Ignore "table talk" but watch the steps for entering the information into a calculator
And...one more example
Classwork: Answer the following questions. Use your graphing calculator to help you.
**Sometimes all the information you need is not given to you. You may need to use the following to help you use the calculator:
a. Find the probability of getting at least 60 heads with 100 flips of a coin (Ans: 0.0287164928)
b. The probability that a team will win a game is 3/5. Use the normal distribution to estimate the probability that the team will win at least 10 of its next 25 games. (Ans:0.9876183243)
Homework: 3-23 odd. Your your graphing calculator to help you find your answers
Binom_prob.JPG
Binom_prob_2.JPG
Answers:
A-binom_prob.JPG
Journal entry: Give an example of an experiment where it is appropriate to use a normal distribution as a approximation for a binomial probability. Explain why in this example an approximation of the probability is a better approach than finding the exact probability.